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angle chasing candidate, inside a right and isosceles triangle

Source: 2014 Oral Moscow Geometry Olympiad grades 8-9 p6

August 9, 2019
geometryanglesAngle Chasingright triangleisosceles

Problem Statement

Inside an isosceles right triangle ABCABC with hypotenuse ABAB a point MM is taken such that the angle ∠MAB\angle MAB is 15o15 ^o larger than the angle ∠MAC\angle MAC , and the angle ∠MCB\angle MCB is 15o15^o larger than the angle ∠MBC\angle MBC. Find the angle ∠BMC\angle BMC .
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